SOLUTION: Find the exact solution when given sinS= 3/5 and cosT = -5/13 where S is in quadrant 2 and T is in quadrant 3. The problem asks to find Cos(S+T) and Tan (S+T) So I used the

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Question 1116545: Find the exact solution when given sinS= 3/5 and cosT = -5/13 where S is in quadrant 2 and T is in quadrant 3.
The problem asks to find Cos(S+T) and Tan (S+T)
So I used the following cos(S)cos(T)-sin(S)sin(T) and tan(S)+tan(T)/1-tan(S)tan(T)

Cos(S+T) = (-4/5)(-5/13)-(3/5)(12/13) = 56/65 (answer)
Tan(S+T) = (3/4)+(-12/5)/1-(3/4)(-12/5) = 33/56 (answer)
I just want to know if those answers are correct or if I made a mistake in getting my values with the given Sin and Cos, especially with my (+/-) decisions. Thank you!
Answer by ikleyn(52804)   (Show Source): You can put this solution on YOUR website!
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Find the exact solution when given sinS= 3/5 and cosT = -5/13 where S is in quadrant 2 and T is in quadrant 3.
The problem asks to find Cos(S+T) and Tan (S+T)
So I used the following cos(S)cos(T)-sin(S)sin(T) and tan(S)+tan(T)/1-tan(S)tan(T) 

Cos(S+T) = (-4/5)(-5/13)-(3/5)(12/13) = 56/65 (answer)    <<<---=== This is absolutely right (!)


Tan(S+T) = (3/4)+(-12/5)/1-(3/4)(-12/5) = 33/56 (answer)  <<<---=== Errors (!): tan(S) = -3/4;  tan(T) = 12/5.   
                                                                    Fix it and everything that follows !


I just want to know if those answers are correct or if I made a mistake in getting my values with  the given Sin and Cos, 
especially with my (+/-) decisions. Thank you!


Find my notices/corrections inside your text.



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